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## Edited by Jessica Argese and Lauren Mazzotta

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**This is a magical tool that you can use to help guide Radius**throughout his journey. You may print out this copy or use your own personal medallion! This story will teach you its special purpose. Have fun and march onward!!!**Aradius is a line segment that joins the center of a circle**with any point on its circumference. Lets look at the picture below! Do you know what Radius’ name means? More than anything, Radius wanted to be a knight. Every day, he practiced riding, sword fighting, and archery. His teacher was brave, old Sir D’Grees. One day, Radius’ parents, Sir Cumference and Lady Di of Ameter, came to watch his lessons. “Show us what you have learned,” they said.**Sir Cumference’s name represents the mathematical term**“circumference.” Do you know the definition of this term? A circumference is the measurement around the perimeter of a circle. Lady Di of Ameter’s name represents the mathematical term “diameter.” Do you know the definition of this term? A diameter is the distance across a circle through its center point.**Before we watch radius’ lesson on right angles,**let’s Review the definition of an angle Angles are formed by two rays that share a common endpoint. Ray Ray**In the riding ring, Radius mounted his horse and Sir**D’Grees gave directions. “Knightly right angle – trot!” shouted Sir D’Grees. Radius rode his horse at a trot to the center of the ring and made an exact right angle turn. It formed a perfect corner. Radius A right angle equals 90° and is formed by two radii of a circle. The special box symbol is used to label right angles! 90° Radius**“Now, double the right angle to make a straight angle!”**called out Sir D’Grees. Radius rode at a full gallop straight across the ring. He came to an abrupt stop right in front of his parents. “Wonderful!” they exclaimed. At supper, Sir D’Grees said, “Radius is ready to go on a quest.” “He is not old enough,” said Sir Cumference looking worried. ----------------------------- What would be the number value of this straight angle? 90 ° 90 ° 180° 90° + 90° = 180°, so two 90° angles make one 180° angle! “I am ready, Father,” he said. “Please let me go.” Sir Cumference slowly looked at each of them. Finally he smiled and nodded.**“Hurrah!” shouted Radius, “But how shall I find**someone in need of help?” “Our neighbor, King Lell, has disappeared,” Sir D’grees answered. “I will search until I find him!” promised Radius. Do you know what this special family medallion is called? It is called a protractor! “Remember your knightly right angle, Radius,” counseled Sir D’Grees. “It will serve you well.” Sir Cumference and Lady Di gave Radius an old family heirloom –a medallion in the shape of a perfect circle.**How to use a Protractor**A protractor is a device used to measure angles from 0 degrees to 180 degrees. The symbol for degrees is a small raised circle (˚). There are two sets of numbers on a protractor so you can measure an angle from either side. In order to choose the correct side, look at the angle that you want to measure. - If it is an obtuse angle (greater than 90˚ and less than 180˚), use the scale that contains numbers greater than 90˚. If it is an acute angle (less than 90˚), use the scale that contains numbers less than 90˚. Click here for a fun Protractor Song When measuring, place the protractor on the angle so that the center point is directly on top of the vertex of the angle and so that one side of the angle lines up with the zero line. Follow the scale, starting at the zero, and read where the other side of the angle intersects with the protractor. This will give you the angle’s measurement. This angle is 60˚ because it intersects with the protractor at the 60 mark! Vertex of an angle Zero line**Investigating angles**Before we continue, let’s review the different types of angles! Match each term to its correct definition! An angle that is equal to 90 degrees Acute Obtuse An angle that is equal to 180 degrees Right An angle that is more than 90 degrees but less than 180 degrees Straight An angles that is less than 90 degrees**Radius bid them farewell and set off. “I’m on a**quest!” he exclaimed gleefully. Radius rode for many days through the countryside. One day, he came upon a tiny village where all the cottages had rooftops pointed in steep angles. “What a quaint, little town,” thought Radius. “Mother would call it ‘cute’.” He asked a villager about King Lell. What types of angles do you spot on the rooftops? These angles are less than 90˚so they are acute angles!!**What types of angles are at the corners of the squares?**Let’s review: How many degrees is a right angle? These squares are made up of right angles! Right angles are 90˚! “His castle lies beyond the Mountains of Obtuse,” said the villager, pointing to the east. “ But take heed! There are tales of strange creatures and dangerous labyrinths.” “Farewell, and thank you” said Radius. He rode through the Mountains of Obtuse. Finally, Radius came upon a walled castle surrounded by a watery moat. He rode cautiously onto the drawbridge. It creaked and groaned with every step. As he neared the middle, the draw bridge began to crumble. Quickly Radius urged his horse across. Just as they reached the other side, the old drawbridge collapsed into the water with a tremendous splash. “That was close!” Radius exclaimed. He rode through the high gates of the castle.**In the courtyard, Radius saw a parchment hanging on a door.**He read the faded writing. Warning, stranger, friend, or foe, Dangers wait as forth you go. You must make a Knightly Right, Finding new Big, Straight, and Slight. Find the Right to reach the kind, Or you will feel the dragon’s sting! The Brothers Zig and Zag What is this angle called? How many degrees is this angle? Itis called a straight angle and it is equal to 180˚. Clutching his medallion, he rode through the doorway into a circular chamber. In the middle of the stone floor, Radius could see a carved circle with a line across its center. All around him, arches led to different rooms. “Which way should I go?” He read from the parchment, “You must make a Knightly Right.” Just then, something flapped out of the shadows and bumped his arm. “Oof!” grunted Radius as his medallion went flying.**90˚**0˚ The medallion rolled away and came to a stop on the carved, stone circle. Radius noticed that the number 90 pointed directly toward one of the arches. “Starting at zero on my medallion, if I go to the center and then to the number 90, that forms a right angle. That’s the knightly right!” he cried. Radius swung himself back onto his horse and rode through the arch that was knightly right, or 90 on the medallion. The way was dark and damp. Around him, unseen things scuttled in the corners. By the light of a flickering candle, Radius read the parchment again. “Find next: Big, Straight, and Slight.”**“What is big?” he wondered. As Radius looked around for**a way out, he saw several hallways. Each had a circle carved in front of it. “If I hold the medallion over a circle, then the number measures the angle to the hallway,” he said. As Radius measured the angle of the two hallways, he found only one that was bigger than a right angle. Measure the angles of both hallways using your protractor. What hallway should Radius go down? We need to find the one that has the “bigger” angle! Determine the measurement of the angle to Hallway 2. _______ Determine the measurement of the angle to Hallway 1. _______ = 55˚ Answer: Hallway 2 = 120˚ Radius entered that hallway, but it ended at a curving stairway. The stairway down was narrow and steep. The stairs came to an end at the fiery pit. Two bridges spanned the inferno. They both started from the same spot, but they crossed the fire pit at different angles.**Let’s apply our knowledge of angles to the world around**us! Which of these objects also contains a “straight angle”? The gas gage or the bird’s beak? Answer: The bottom of the gas gage is an 180˚ angle! A straight angle equals 180˚. “After ‘Big,’ the parchment reads ‘Straight,” Radius remembered. “That’s 180 on my medallion. You can’t get an angle straighter than that!” He took a deep breath and ran across the bridge that went straight over the roaring fire. On the other side, Radius heaved a sigh of relief. He opened a heavy door and entered a dark tunnel. The door clanged shut behind him.**Raspy snuffling came from deep within the darkness. Four**glowing eyes appeared and began moving slowly toward him. Clutching his medallion, Radius hurtled down the tunnel. What hallway should Radius go down? We need the smallest angle! The smallest angle is 40˚. The tunnel ended. Other tunnels shot off at different angles. In front of each was a carved circle glowing with its own light. “The parchment says a ‘Slight’ angle,” Radius mumbled, “like the rooftops in that cute little village I passed through. A cute little angle is what I need, something less than 90 on the medallion.” The smallest angle measured 40, so he turned there.**Radius ran through the darkness. “Next will be the**‘Right to reach the king’ – another knightly right angle of 90. “At least the last angle will be easy,” he gasped. He was wrong. In the dim light, he came across four corridors which all seemed to be right angles! Fingers fumbling, he measured quickly with the medallion – 90, 90, 90 – and 90 again! What are the values of these angles? 85˚ 93˚ 90˚ Can you see how Radius might have thought that these angles were all 90˚ at a quick glance?! 89˚ “Slow down,” Radius told himself, “and measure once more.” He carefully lined up the medallion and read the numbers. The first angle was 93. “Too big,” he said. The next angle was 85. “too small,” he muttered. The third one was 89. “Almost right,” he said. Then there was a great whooshing sounds and thick smoke filled the tunnel.**Radius was caught inside a dark cloud. Coughing and**sputtering, he felt his way along to the remaining corridor. “I hope this is the one,” he whispered. THUMP -THUMP - THUMP. Something was lurching toward him. Suddenly, Radius ran into a wall of stone. He was trapped! The thumping grew louder. Whatever it was, it was big and it was right behind him! What are these “cute little angles” called? Acute angles!! Radius turned around and stood with his back to the wall. His arm bumped into…a latch…a handle…he pushed with all his strength, and a door swung open.**Brilliant sunshine met his eyes. “Welcome!” a voice**bellowed. “Who might you be?” “I am Radius, son of Sir Cumference and Lady Di of Ameter, and squire to Sir D’Grees. I am searching for King Lell.” “It seems you have found him,” chuckled the king. Radius bowed, “My medallion helped me figure out which paths to take.” Can you recall what type of mathematical tool Radius’ medallion is? What is it called? A protractor! Why is a protractor useful? Protractors help people measure angles from 0˚ to 180˚ in degrees. Protractors can also be used to construct angles. A whimpering came from behind the door. King Lell opened it wider. Radius jumped back. “Dragons!” he gulped. “They are my loyal pets,” explained the king. He scratched their heads. “The poor beasts and I were trapped in the maze by my evil cousins Zig and Zag but we are free now.” He continued, “Young squire, anyone brave enough and smart enough to figure out that maze deserves his knighthood!”**What are the names of the highlighted angles?**Obtuse There are more examples of these angles that can be found on this page, can you find them? Acute Straight angle Right When King Lell whistled and called out, “Pair of Lells!”, the two dragons stretched across the moat, side by side. They became a living drawbridge for the guests to cross.**Did you know that there are other types of angles called**supplementary and complementary angles? What are their definitions? Supplementary angles are two angles that add up to 180˚. Just think… “s” for supplementary stands for “s” in straight angle. Therefore, supplementary angles always add up to 180˚. Complementary angles are two angles that add up to 90˚. Just think… “c” for complementary stands for “c” in corner. Right angles are at the corners of squares! Therefore, complementary angles always add up to 90˚. With Radius’s medallion, they easily found their way back through the maze. To celebrate King Lell’s freedom, invitations were sent to all the neighboring knights and ladies. Sir Cumference, Lady Di of Ameter, and even old Sir D’Grees came. Radius and King Lell went to the moat to greet each group of guests.**Radius explained his success: “I discovered the secret of**the medallion! The numbers divide a circle into 360 parts. I can use those parts to measure any angle. I call the parts of a circle degrees in honor of my teacher, Sir D’Grees.” Complementary Angles 65˚ 100˚ 25˚ 80˚ Supplementary Angles Radius drew a picture of his medallion and took an arrow from his quiver. “Let’s say this arrow points to a hallway. The number shows how many degrees. A straight line measures 180 degrees. I call angles bigger than 90 degrees obtuse after the Mountains of obtuse. Angles smaller than 90 I call acute. They look like the roofs in a small village I traveled through.”**Calculate the missing value of this supplementary angle (in**degrees). Write your answer on the pink box below. Calculate the missing value of this complementary angle (in degrees). Write your answer on the green box below. Answer: 150˚ Answer: 30˚ King Lell told Radius to kneel. “For your bravery and intelligence, I knight you Sir Radius!” the king proclaimed. “From this day forth, let this Kingdom be called Angleland. Banners will fly on every castle tower! They shall show knightly right angles of 90 degrees, small acute angles, large obtuse angles, and straight angles of 180 degrees. Rise now, great knight of Angleland!” The crowd cheered, and Radius rose to greet them.**Angleland was the only kingdom to have a castle with a**living drawbridge. The cry “Pair of Lells!” brought the two dragons over the moat. They became so famous that today parallel means any straight lines side by side, the same distance apart, like the Lell Dragons. Angleland is still there on very old maps, but today we call it England. Use your protractor to create your own supplementary angle on the line provided below! Write each angle’s value in degrees. • Some possible answers include but are not limited to: • 40 ˚ and 120 ˚ • 110 ˚ and 70 ˚ • 145 ˚ and 35 ˚ These Lell dragons create parallel lines. Parallel lines never intersect and go on forever.**Let’s review Everything that radius has taught us!**What is a radius? A radius is a line segment that joins the center of a circle with any point on its circumference. What is the circumference of a circle? What is the diameter of a circle? A diameter is the distance across a circle through its center point A circumference is the measurement around the perimeter of a circle.**Match the types of angles in Column A to the correct image**in Column B Column A Column B Right Angle Acute Angles Obtuse Angles Straight Angle**Column B**Column A Complementary Angle Supplementary Angle Parallel Lines**The End**Radius wants to thank you for helping him on his mathematical journey!